Question 1182962


let numerator be {{{x}}}
if the denominator  is {{{9}}} more than  numerator, the denominator  is {{{x+9}}}

fraction is:
{{{x/(x+9)}}}

if the numerator and the denominator both are increased by {{{7}}}, the new fraction becomes {{{10/7}}} 

{{{(x+7)/(x+9+7)=10/7}}}............solve for {{{x}}}

{{{(x+7)/(x+16)=10/7}}}...., cross multiply

{{{7(x+7)=10(x+16)}}}

{{{7x+49=10x+160}}}

{{{49-160=10x-7x}}}

{{{-111=3x}}}

{{{x=-111/3}}}

{{{x=-37}}}-> numerator

the denominator  is {{{x+9=-37+9=-28}}}

the original fraction is {{{highlight(-37/-28)}}}


check: the numerator and the denominator both are increased by {{{7}}}

{{{highlight((-37+7)/(-28+7))=10/7}}}
{{{highlight((-30)/(-21))=10/7}}}
{{{highlight(30/21)=10/7}}}
{{{highlight(10/7)=10/7}}}